2. Finish solving each IVP by finding y(t), the inverse transform of Y(s). Do not use convolution here. [8] a) "+6y8y = 2, y(0)=-2, y'(0) = 1. Taking Laplace transforms gives 2 2 s2Y(s) + 28 1+6(sY(s)+2)+8Y(s) = = = => Y(s) = + S s(82 +68+8) -11-28 $2 +68+8
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- 3. (a) Calculate the Laplace transform of each function. Explain your reasoning (i) cos(2t) sin(4t). (ii) est cosh(3t). (iii) H(t-2) sin(4t-8). (iv) (t-3)²e-2tH(t-3).Find the Fourier transform of sinc(t). (a) rect() (b) T rect() 3. 27T (c) T rect() (d) ㅠ rect(은) O e) Moving to another quEstion will eave this reaponse. Type here to search 3/5Find the Fourier transform of sinc (2t). (a) 2n A(w/2) 3. (b) п Д(u/4) A(w/8 (d) A(w/16) Moving to the next ouestion.prevents changes to chis anaWer
- Q)find the inverse Laplace transform (3 L-' (P²t1) P-1 (4) L- 2P (P²-1)²Q1) Find Fourier transform for the following functions: a) x(t) = 3 + (sin2wt)? b) y(t) = 5. (e-6t). 8(t – 8) + 6u(t + 8) %3D2s +3 Find the Inverse Laplace Transform of (s+4)3 1 -2" (cos2t + -sin2t) 2 A e 1 "(2cos2t + - sin2t) 2 (c) 1 e2" (2sin2t + -cos2t) 2 D e-2" (2cos2t + sin2t) B.
- Q3) a) Find Laplace transform of the following functions 1- f(t) = e2t cos(t) 2- f(t) = t sinh(2t) %3D b) Find inverse Laplace transform of the function 7s – 1 F(s) = (s + 1)(s + 2)(s – 3) 12. Find inverse Fourier transform of F(W) = W2-2W+3Solve the following equations show your solutions. 1. Find the equation of a line perpendicular to y = 1 through A(-1, 1). 2. Find the area of the circle with center at (1, 3) and tangent to the line 5x - 12y - 8 = 0. 3. Determine the Inverse Laplace Transform of F(s) = (s + 2)(e^-s)/(s^2 + 4).